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by Stuart@KaplanGMAT » Wed Apr 14, 2010 10:22 am
pradeepkaushal9518 wrote:What is the units digit of 6to power15 - 7to power4 - 9 to power3?
A) 8
B) 7
C) 6
D) 5
E) 4


answer is C but dont know how anyone can explain
We want the units digit of : (6^15 - 7^4 - 9^3)

The first thing we should note is that there's no way we're expected to actually calculate this giant mess of a number. So, there must be a shortcut.

We think: I only care about the last digit of the number; so, if I can find a quick way to calculate final digit, I'm home free.

Now, let's look for patterns:

6^1 = 6
6^2 = 36
6^3 = 216

hey! Every power of 6 ends in 6.

7^1 = 7
7^2 = 49
7^3 = ...3
7^4 = ...1

9^1 = 9
9^2 = 81
9^3 = ..9

So, putting that into our expression:

(...6) - (...1) - (...9) = (...5) - (...9) = (...6)

choose C!
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by pradeepkaushal9518 » Thu Apr 15, 2010 6:05 am
thanks mr stuart but 5-9 = 6 is not clear can u please explain that part
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by eaakbari » Thu Apr 15, 2010 6:25 am
pradeepkaushal9518 wrote:thanks mr stuart but 5-9 = 6 is not clear can u please explain that part
There is a carry over from the 10s digit , so it becomes 15-9 = 6
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